function [name,T,y,u,ys,us,ysu,usu] = ppp_ex21 (ReturnName)
## usage: ppp_ex21 ()
##
## PPP example - 2nd-order 2i2o system system with anomalous behaviour"
## $Id$
## Example name
name = "2nd-order 2i2o system with anomalous behaviour"
if nargin>0
return
endif
## System
A = [-2 -1
1 0];
B = [[1;0], [1;2]];
C = [ [0,1]; [2,1]];
D = zeros(2,2);
sys = ss2sys(A,B,C,D);
[n_x,n_u,n_y] = abcddim(A,B,C,D);
## Display it
for j = 1:n_u
for i = 1:n_y
sysout(sysprune(sys,i,j),"tf")
step(sysprune(sys,i,j),1,5);
endfor
endfor
## Setpoint
A_w = 0;
## Controller
##Optimisation horizon
t =[4:0.1:5];
## A_u
pole = [4];
#A_u = ppp_aug(laguerre_matrix(2,pole),0);
#A_u = ppp_aug(diag([-3,-4]),0);
A_u = ppp_aug(butterworth_matrix(2,pole),0);
Q = ones(n_y,1);;
## Setpoints
W = [1:n_y]';
## Initial condition
x_0 = [0;0.5];
## Design and plot
[ol_poles,cl_poles,ol_zeros,cl_zeros,k_x,k_w,K_x,K_w,cond_uu] = ppp_lin_plot (A,B,C,D,A_u,A_w,t,Q,W,x_0);
format short
cl_poles
A_c = A-B*k_x; # Closed-loop A
A_cw = [A_c B*k_w*W
zeros(1,n_x+1)]
log_cond_uu = log10(cond_uu)
# K_xwe = ppp_open2closed(A_u,A_cwe,[k_xe -k_we*W]); # Exact Kx
#AA_u = ppp_inflate([A_u;A_u]);
K_xwc = ppp_open2closed(A_u,A_cw,[k_x -k_w*W]) # Computed Kx
# Exact_K_xw = K_xwe
Approx_K_xw = [K_x -K_w*W]
format
endfunction